To be honest – I’ve only spent half a day on Venice. There is obviously a lot to do. I suggest just walking around and getting lost. Obviously at some point make sure you wander your way towards St. Mark’s Square, the Ponte di Rialto (pictured), and the Ponte di Sospiri (the famous “bridge of sighs” – the walkway which prisoners headed to the cells had to walk across and from which they glimpsed their last look on the outside world).
Unfortunately no restaurant recommendations, as the city is flooded with tourists. More tourists = worse food served (since majority of American/British tourists don’t know/care about authentic food if it wacked them upside the head).
Another tidbit – regardless of the hype, Venice IS a romantic city. Visiting it alone will be OK, but you may be lonely. Visiting with friends does it no justice. Go with someone you care about/have intimate feelings for – the experience will be all the more better.